We introduce a new measure of the discrepancy in strategic games between the social welfare in a Nash equilibrium and in a
social optimum, that we call selfishness level. It is the smallest fraction of the social welfare that needs to be offered
to each player to achieve that a social optimum is realized in a pure Nash equilibrium. The selfishness level is unrelated
to the price of stability and the price of anarchy and is invariant under positive linear transformations of the payoff functions.
Also, it naturally applies to other solution concepts and other forms of games.

We study the selfishness level of
several well-known strategic games. This allows us to quantify the implicit tension within a game between players' individual
interests and the impact of their decisions on the society as a whole. Our analyses reveal that the selfishness level often
provides a deeper understanding of the characteristics of the underlying game that influence the players' willingness to cooperate.

In particular, the selfishness level of finite ordinal potential games is finite, while that of weakly acyclic games can be
infinite. We derive explicit bounds on the selfishness level of fair cost sharing games and linear congestion games, which
depend on specific parameters of the underlying game but are independent of the number of players. Further, we show that the
selfishness level of the $n$-players Prisoner's Dilemma is c/(b(n-1)-c), where b and c are the benefit and cost for cooperation,
respectively, that of the n-players public goods game is (1-c/n)/(c-1), where c is the public good multiplier, and that of
the Traveler's Dilemma game is (b-1)/2, where b is the bonus. Finally, the selfishness level of Cournot competition (an example
of an infinite ordinal potential game), Tragedy of the Commons, and Bertrand competition is infinite.

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